katzcent: Find the Katz centrality (Katz Status Index)
In centiserve: Find Graph Centrality Indices

Description Usage Arguments Details Value Author(s) References Examples

The Katz centrality for node i is:

x(i)=alpha * sum(A(ij)*x(j), j) + beta

where A is the adjacency matrix of the graph G with eigenvalues lambda. The parameter beta controls the initial centrality and alpha < 1/lambda(max).

1	katzcent(graph, vids = V(graph), alpha = 0.1)

`graph`	The input graph as igraph object
`vids`	Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices.
`alpha`	The alpha parameter, which must be between 0.0-0.2. The default is 0.1.

Katz centrality computes the relative influence of a node within a network by measuring the number of the immediate neighbors (first degree nodes) and also all other nodes in the network that connect to the node under consideration through these immediate neighbors.
More detail at Katz Centrality

A numeric vector contaning the centrality scores for the selected vertices.

Mahdi Jalili m_jalili@farabi.tums.ac.ir

Algorithm adapted from CentiBin with thanks Dirk Koschutzki. (Junker, Bjorn H. 2006).

Newman, Mark. Networks: an introduction. Oxford University Press, 2010.

Junker, Bjorn H., Dirk Koschutzki, and Falk Schreiber. "Exploration of biological network centralities with CentiBiN." BMC bioinformatics 7.1 (2006): 219.

1 2	g <- barabasi.game(20) katzcent(g)

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: Matrix
 [1] 1.874 1.200 1.230 1.110 1.000 1.000 1.000 1.100 1.000 1.100 1.300 1.000
[13] 1.000 1.000 1.100 1.000 1.000 1.000 1.000 1.000